Access the full text.
Sign up today, get DeepDyve free for 14 days.
N. Aubry, J. Lumley, P. Holmes (1990)
The effect of modeled drag reduction on the wall regionTheoretical and Computational Fluid Dynamics, 1
A. Papoulis (1965)
Probability, Random Variables and Stochastic Processes
O. Reynolds (1995)
On the dynamical theory of incompressible viscous fluids and the determination of the criterionProceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 451
(1989)
Kuramoto-Sivashinksy dynamics on the center mastable manifold
Lawrence Sirovich, Bruce Knight (1985)
The eigenfunction problem in higher dimensions: Asymptotic theory.Proceedings of the National Academy of Sciences of the United States of America, 82 24
G. Berkooz, P. Holmes, J. Lumley (1993)
On the relation between low-dimensional models and the dynamics of coherent structures in the turbulent wall layerTheoretical and Computational Fluid Dynamics, 4
C. Foias, M. Jolly, I. Kevrekidis, E. Titi (1991)
Dissipativity of numerical schemesNonlinearity, 4
P. Moin, R. Adrian, J. Kim (1987)
Stochastic estimation of organized structures in turbulent channel flow
P. Holmes (1993)
Symmetries, Heteroclinic Cycles and Intermittency in Fluid Flow, 55
S. Robinson (1991)
Coherent Motions in the Turbulent Boundary LayerAnnual Review of Fluid Mechanics, 23
K. Lii, M. Rosenblatt, C. Atta (1976)
Bispectral measurements in turbulenceJournal of Fluid Mechanics, 77
R. Adrian, P. Moin, R. Moser (1987)
Stochastic estimation of conditional eddies in turbulent channel flow
L. Sirovich (1987)
Turbulence and the dynamics of coherent structures. I. Coherent structuresQuarterly of Applied Mathematics, 45
V. Algazi, D. Sakrison (1969)
On the optimality of the Karhunen-Loève expansion (Corresp.)IEEE Trans. Inf. Theory, 15
A. Duggleby, K. Ball, M. Paul, P. Fischer (1991)
Dynamical eigenfunction decomposition of turbulent channel flowInternational Journal for Numerical Methods in Fluids, 12
M. Glauser, S. Leib, W. George (1987)
Coherent Structures in the Axisymmetric Turbulent Jet Mixing Layer
M. Glauser, W. George (1987)
An orthogonal decomposition of the axisymmetric jet mixing layer utilizing cross-wire velocity measurements
E. Stone, P. Holmes (1990)
Random perturbations of heteroclinic attractorsSiam Journal on Applied Mathematics, 50
P. Constantin, C. Foias, B. Nicolaenko, R. Téman (1988)
Integral Manifolds and Inertial Manifolds for Dissipative Partial Differential Equations
P. Holmes, E. Stone (1992)
Heteroclinic Cycles, Exponential Tails, and Intermittency in Turbulence Production
(1992)
The wavelet transform and its applications to fluid mechanics
H. Park, L. Sirovich (1990)
Turbulent thermal convection in a finite domain: Part II. Numerical resultsPhysics of Fluids, 2
(1990)
Application of the Karhunen-Lo~ve
R. Antonia (1981)
Conditional Sampling in Turbulence MeasurementAnnual Review of Fluid Mechanics, 13
S. Rice (1944)
Mathematical analysis of random noiseBell System Technical Journal, 23
W. Feller (1959)
An Introduction to Probability Theory and Its Applications
D. Anderson, J. Tannehill, R. Pletcher (2020)
Computational Fluid Mechanics and Heat Transfer
J. Lumley (1970)
Stochastic tools in turbulence
L. Sirovich, H. Park (1990)
Turbulent thermal convection in a finite domain: Part I. TheoryPhysics of Fluids, 2
H. Bartelt, A. Lohmann, B. Wirnitzer (1984)
Phase and amplitude recovery from bispectra.Applied optics, 23 18
(1987)
The dimension of an attractor in turbulent Poiseuille flow
S. Campbell, P. Holmes (1992)
Heteroclinic cycles and modulated travelling waves in a system with D 4 symmetryPhysica D: Nonlinear Phenomena, 29
K. Promislow (1991)
Time analyticity and Gevrey regularity for solutions of a class of dissipative partial differential equationsNonlinear Analysis-theory Methods & Applications, 16
R. Preisendorfer, C. Mobley (1988)
Principal Component Analysis in Meteorology and Oceanography
J. Liu (1988)
Contributions to the understanding of large-scale coherent structures in developing free turbulent shear flowsAdvances in Applied Mechanics, 26
G. Palade, Albert Claude
THE NATURE
H. Moffatt (1990)
Fixed points of turbulent dynamical systems and suppression of nonlinearity
J. Jiménez, P. Moin (1991)
The minimal flow unit in near-wall turbulenceJournal of Fluid Mechanics, 225
Michael Kirby, L. Sirovich (1990)
Application of the Karhunen-Loeve Procedure for the Characterization of Human FacesIEEE Trans. Pattern Anal. Mach. Intell., 12
G. Berkooz (1991)
Turbulence, Coherent Structures, and Low-Dimensional Models.
J. Rodriguez, L. Sirovich (1990)
Low-dimensional dynamics for the complex Ginzburg-Landau equationPhysica D: Nonlinear Phenomena, 43
(1963)
Variability of energy dissipation rate in a turbulent flow and the energy
(1991)
The POD systems with symmetry and harmonic analysis Coherent structures in random media and wavelets Intermittent dynamics in simple models of the wall layer
(1991)
A computational study of Rayleigh-B6nard
A. Deane, L. Sirovich (1991)
A computational study of Rayleigh–Bénard convection. Part 1. Rayleigh-number scalingJournal of Fluid Mechanics, 222
D. Ruelle, F. Takens (1971)
On the nature of turbulenceCommunications in Mathematical Physics, 20
J. Lumley (1990)
Whither Turbulence? Turbulence at the Crossroads, 357
(1945)
Functions aleatoire de second
R. Adrian (1979)
Conditional eddies in isotropic turbulencePhysics of Fluids, 22
D. Armbruster, J. Guckenheimer, P. Holmes (1988)
Heteroclinic cycles and modulated traveling waves in systems with O(2) symmetry
L. Sirovich, M. Kirby (1986)
Low-dimensional Procedure for the Characterization of Human Faces
L. Sirovich (1989)
Chaotic dynamics of coherent structuresPhysica D: Nonlinear Phenomena, 37
D. Stretch, J. Kim, R. Britter (1990)
A conceptual model for the structure of turbulent channel flow
N. Aubry, S. Sanghi (1991)
Bifurcations and bursting of streaks in the turbulent wall layer
(1989)
Gevrey class regularity lbr the solutions of the NavierStokes
(1989)
Periodic wavelet analysis: a tool for inhomogeneous
王碧祥 (1994)
APPROXIMATE INERTIAL MANIFOLDS TO THE NAVIER-STOKES EQUATIONS
(1993)
Downloaded from arjournals.annualreviews.org by LEICESTER UNIVERSITY LIBRARY on 12/30/07. For personal use only
N. Platt, L. Sirovich, N. Fitzmaurice (1990)
An investigation of chaotic Kolmogorov flowsPhysics of Fluids, 3
Michael Kirby, J. Boris, L. Sirovich (1990)
A proper orthogonal decomposition of a simulated supersonic shear layerInternational Journal for Numerical Methods in Fluids, 10
P. Moin, R. Moser (1989)
Characteristic-eddy decomposition of turbulence in a channelJournal of Fluid Mechanics, 200
L. Sirovich, B. Knight, J. Rodriguez (1990)
Optimal low-dimensional dynamical approximationsQuarterly of Applied Mathematics, 48
S. Pope (1985)
PDF methods for turbulent reactive flowsProgress in Energy and Combustion Science, 11
C. Foias, G. Sell, E. Titi (1989)
Exponential tracking and approximation of inertial manifolds for dissipative nonlinear equationsJournal of Dynamics and Differential Equations, 1
Toshifumi Matsuoka, T. Ulrych (1984)
Phase estimation using the bispectrumProceedings of the IEEE, 72
D. Stretch (1991)
Automated pattern eduction from turbulent flow diagnostics
J. Math. Anal. Appl
A. Townsend (1979)
Flow patterns of large eddies in a wake and in a boundary layerJournal of Fluid Mechanics, 95
N. Aubry, R. Guyonnet, R. Lima (1991)
Spatiotemporal analysis of complex signals: Theory and applicationsJournal of Statistical Physics, 64
D. Chambers, RJ. Adrian, P. Moin, Ds Stewart, H. Sung (1988)
Karhunen-Loeve expansion of Burgers' model of turbulencePhysics of Fluids, 31
(1991)
Statistical analysis of phase portraits: bifurcations and perturbations of limit cycles..Preprint
E. Stone, P. Holmes (1991)
Unstable fixed points, heteroclinic cycles and exponential tails in turbulence productionPhysics Letters A, 155
L. Sirovich, K. Ball, L. Keefe (1990)
Plane waves and structures in turbulent channel flowPhysics of Fluids, 2
S. Sanghi, N. Aubry (1992)
Mode interaction models for near-wall turbulenceJournal of Fluid Mechanics, 247
N. Kampen (1985)
Elimination of fast variablesPhysics Reports, 124
S. Kline, W. Reynolds, F. Schraub, P. Runstadler (1967)
The structure of turbulent boundary layersJournal of Fluid Mechanics, 30
N. Aubry, P. Holmes, J. Lumley, E. Stone (1988)
The dynamics of coherent structures in the wall region of a turbulent boundary layerJournal of Fluid Mechanics, 192
(1967)
The structure ofinhomogeneous turbulence Stochastic Tools in Turbulence Coherent structures in turbulence The state of turbulence research
Xiaowei Zheng, M. Glauser (1990)
Low dimensional description of the axisymmetric jet mixing layer
W. Ray (1987)
Identification and Control of Linear Distributed Parameter Systems Through the Use of Experimentally Determined Singular FunctionsIFAC Proceedings Volumes, 20
A. Townsend (1975)
The Structure of Turbulent Shear Flow
Ross Williams (1990)
Adaptive Data Compression
K. Sreenivasan, A. Prabhu, R. Narasimha (1983)
Zero-crossings in turbulent signalsJournal of Fluid Mechanics, 137
A. Johansson, P. Alfredsson (1982)
On the structure of turbulent channel flowJournal of Fluid Mechanics, 122
(1953)
General theory of the correlations of random functions
H. Liepmann (1952)
Aspects of the turbulence problemZeitschrift für angewandte Mathematik und Physik ZAMP, 3
A. Rosenfeld, A. Kak (1976)
Digital Picture Processing
M. Glauser, W. George (1987)
Orthogonal Decomposition of the Axisymmetric Jet Mixing Layer Including Azimuthal Dependence
E. Stone (1989)
A study of low-dimensional models for the wall region of a turbulent boundary layer
(1989)
lntegral Manifolds and Inertial Manifolds
R. Temam (1993)
Infinite Dimensional Dynamical Systems in Mechanics and Physics Springer Verlag
D. Bogard, W. Tiederman (1986)
Burst detection with single-point velocity measurementsJournal of Fluid Mechanics, 162
N. Aubry, Wen Lian, E. Titi (1993)
Preserving Symmetries in the Proper Orthogonal DecompositionSIAM J. Sci. Comput., 14
M. Glauser, Xiaowei Zheng, C. Doering (1991)
The Dynamics of Organized Structures in the Axisymmetric Jet Mixing Layer
Michael Kirby, J. Boris, L. Sirovich (1990)
An eigenfunction analysis of axisymmetric jet flowJournal of Computational Physics, 90
A. Deane, I. Kevrekidis, G. Karniadakis, S. Orszag (1991)
Low‐dimensional models for complex geometry flows: Application to grooved channels and circular cylindersPhysics of Fluids, 3
J. Proakis (1985)
Probability, random variables and stochastic processesIEEE Trans. Acoust. Speech Signal Process., 33
(1989)
Gevrey class regularity lbr the solutions of the Navier- Stokes equations Exponential tracking and approximation of inertial manifolds for dissipative equations
C. Foias, O. Manley, L. Sirovich (1990)
Empirical and Stokes eigenfunctions and the far‐dissipative turbulent spectrumPhysics of Fluids, 2
A. Glezer, Zafer Kadioglu, A. Pearlstein (1989)
Development of an extended proper orthogonal decomposition and its application to a time periodically forced plane mixing layerPhysics of Fluids, 1
J. Lumley (1981)
Coherent Structures in Turbulence
D. Brillinger, M. Rosenblatt (1967)
ASYMPTOTIC THEORY OF ESTIMATES OF kTH-ORDER SPECTRA.Proceedings of the National Academy of Sciences of the United States of America, 57 2
G. Berkooz, J. Elezgaray, P. Holmes (1992)
Coherent structures in random media and waveletsPhysica D: Nonlinear Phenomena, 61
W. Ray (1988)
Application of singular value methods for identification and model based control of distributed parameter systemsIFAC Proceedings Volumes, 21
(1957)
On the application of functional calculus to the statistical theory of turbulence
(1991)
Reconstructing phase space for PDE
R. Adrian, P. Moin (1988)
Stochastic estimation of organized turbulent structure: homogeneous shear flowJournal of Fluid Mechanics, 190
(1946)
Zur spektral theorie stochastischer prozesse
(1991)
Turbulence , dynamical systems and the unreasonable effectiveness of empirical cigenfunctions
(1954)
Statistical description of continuous fields
L. Sirovich, Michael Kirby, M. Winter (1990)
An eigenfunction approach to large scale transitional structures in jet flowPhysics of Fluids, 2
P. Bradshaw (1971)
The Physics of Turbulence
L. Sirovich, A. Deane (1991)
A computational study of Rayleigh–Bénard convection. Part 2. Dimension considerationsJournal of Fluid Mechanics, 222
John Kim, P. Moin, R. Moser (1987)
Turbulence statistics in fully developed channel flow at low Reynolds numberJournal of Fluid Mechanics, 177
J. Fluid Mech
L. Sirovich (1991)
Empirical Eigenfunctions and Low Dimensional Systems
R. Blackwelder, R. Kaplan (1976)
On the wall structure of the turbulent boundary layerJournal of Fluid Mechanics, 76
M. Glauser, Xiaowei Zheng, W. George (1992)
The Streamwise Evolution of Coherent Structures in the Axisymmetric Jet Mixing Layer
G. Berkooz (1992)
Observations on the Proper Orthogonal Decomposition
1.1 The Problems of Turbulence It has often been remarked that turbulence is a subject of great scientific and technological importance, and yet one of the least understood (e.g. McComb 1990). To an outsider this may seem strange, since the basic physical laws of fluid mechanics are well established, an excellent mathematical model is available in the Navier-Stokes equations, and the results of well over a century of increasingly sophisticated experiments are at our disposal. One major difficulty, of course, is that the governing equations are nonlinear and little is known about their solutions at high Reynolds number, even in simple geometries. Even mathematical questions as basic as existence and uniqueness are unsettled in three spatial dimensions (cf Temam 1988). A second problem, more important from the physical viewpoint, is that experiments and the available mathematical evidence all indicate that turbulence involves the interaction of many degrees of freedom over broad ranges of spatial and temporal scales. One of the problems of turbulence is to derive this complex picture from the simple laws of mass and momentum balance enshrined in the NavierStokes equations. It was to this that Ruelle & Takens (1971) contributed with their suggestion that turbulence
Annual Review of Fluid Mechanics – Annual Reviews
Published: Jan 1, 1993
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.